https://en.wikipedia.org/wiki/Variance#Sum_of_uncorrelated_variables_.28Bienaym.C3.A9
_formula.29
Photoreceptor response to a light flash is a change in voltage across
the cell membrane.
The voltage (or potential difference) itself is caused by a difference
in ion concentration (e.g. sodium, potassium, calcium) between
the inside and outside of the cell.
intensity of flash
Nerve cells communicate across "synapses". The pre-synaptic cell
releases a hormone ("neurotransmitter") which is taken up by postsynaptic cell, and causes the post-synaptic cell to increase its voltage
(excitatory) or decrease its voltage (inhibitory).
Details omitted because this isn't a physiology course !
McCulloch-Pitts Model of Neuron Response (1943)
This was the starting point for what's now known as neural networks.
https://askabiologist.asu.edu/neuron-anatomy
Input to cell happens at the dendrites.
Output signal (wave) is sent along the axon.
http://www.youtube.com/watch?v=ifD1YG07fB8
In visual system, an axon might be several cm.
In motor system, an axon can be ~1 meter (spinal cord).
dendrites
(input)
cell body
(computation)
axon
(output)
Spike Train
Neurons in the brain communicate over distances by
sending pulses (spikes) away from the cell body and along
the axon.
A sequence of pulses is called a "spike train".
"Electrophysiology": measure the spike trains and try to
"decode" what the cell is communicating.
Analogy: The heart pumps blood. You can measure the
heart beat rate by taking your pulse.
Typical spike rates ("firing rates") are 0-100 spikes/sec.
"Receptive field" of a cell
Classical Theory of Spikes
- The detailed shape of the spike (e.g. height)
doesn't matter.
Experiments in early 1950's on cat retinal
ganglion cells:
- The speed at which the spike moves along the axon is
constant for each cell (but will differ between cell types
e.g. when you stub your toe, you notice the impact
and then the pain ).
- The "cell response" to a stimulus is is the spike frequency
(or "rate"). The precise timing of spikes doesn't matter
(but modern theory disputes this as we will see later)
- If stimulus is held constant, then the spike firing rate
gradually will decrease to a baseline "firing rate
(not zero).
This is a form of adaptation.
Retinal ganglion cells are either:
- region of visual field (xy) that can affect the cell's firing
rate
This is often called "lateral inhibition" (even though the
one of the right might be called lateral excitation)
It is often modelled as a DOG function (last lecture).
Mechanism
Peripheral vision is less sensitive to fine details. Why?
- fewer cones/mm^2
- ganglion cell receptive fields are larger
(hence sensitive to more lower frequencies)
- optics is not as good in the periphery
Spike Train
Suppose we model the nerve cell response as follows.
We can think of f(x,y,t) as an impulse response function. To discover what f( ) is for
given cell, we could let the stimulus I( ) be a set of impulse functions (flash of light at
some position and time) and look at the firing rate of the cell for each impulse.
Unfortunately, that doesn't work in practice. Retinal ganglion cells (and other cells
deeper in the visual system) don't respond reliably to small flashes of light.
Even if they did, the responses are spike trains, not continuous functions.
Method 1: "Peristimulus time histogram"
How can one estimate an impulse response function
f(x,y,t) for a given cell, and what does it mean ?
The example below doesn't show the stimulus. It only
shows the spike trains (40) and their sum, which is
taken as the average response to the stimulus.
Only sketching dependence of I(x,y,t) on
time here, but there is also a
dependence on (x,y), i..e its a video
Spike train responses r(t) of that cell to
many instances of that stimulus I(x,y,t)
Experimenter tries to figure out what function f(x,y,t) best explains the
responses, given the chosen stimulus I(x,y,t) which was repeatedly used.
Adding up all these spike trains gives us a
histogram of reponses, namely the total
number of spikes in each time bin:
Modern Theory of Spikes
One issue is, how to choose I(x, y, t) so that f(x, y, t) is most reliable ?
Method 2: "Spike triggered average"
Here is an example of the average video that produced a spike in
a retinal ganglion cell. Notice that for more than ~150 ms before
the spike, the averages all cancel out to ~0.
- The detailed shape of the spike (e.g. height)
doesn't matter.
- The speed at which the spike moves along the axon is
constant for each cell but will differ between cell types
- The "cell response" to a stimulus is is the spike frequency
(or "rate"). The precise timing of spikes doesn't matter
The precise timing of spikes matters.
t
(ms)
YOU WILL NOT BE EXAMINED ON THIS.
x (position)